Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If θ is the angle (semi-vertical) of a cone of maximum volume and given slant height, then tan θ is given by
A
2
B
1
C
D
Text Solution
Verified by ExpertsThe correct answer is:
C
Let OB = λ , OA = λ cos θ and AB = λ sin θ ( 0 ≤ θ ≤ π /2). Then
V = 
(AB) 2 (OA) = 
λ 3 sin 2 θ cos θ
⇒ 
= 
λ 3 sin θ (3 cos 2 θ –1)
So from 
= 0, we get θ = 0 or cos θ = 
. Also V(0) = 0, V ( π /2) = 0 and
V 
= 
Hence V is maximum when cos θ = 1/ 
, i.e.,
tan θ = 
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